Apologize, and share some of your history. How much you should share depends on how close the relationship is. But just admitting that you lied is not enough; you need to actually apologize and make sure she knows that you are going to work toward being more honest.

At the end of the day, whilst honesty is important, I think if she is unwilling to see that it was a white lie told only to please her (as youve alluded too) she needs to take a long look at her priorities in life.